Case Study 9

Probability, Simulation, and Expected Value

31 Points Possible

1. A probability model is given below for the percentage of Nigeria's citizens with each blood type (ignoring + and -). Fill in the probability (1 point):

O	A	B	AB
0.53		0.21	0.03

1. List the digits you would use to represent each blood type for a simulation (3 points).

O =

A =

B =

AB =

1. What is your simulated probability of a visitor having Type B blood (1 point)? _______

1. Why do you think a simulation like this would be helpful for a Nigerian blood bank? In other words, what could a blood bank do with the results of this simulation (3 points)?

1. A sample of individuals who voted in the 2018 midterm elections demonstrated the following breakdown by political party. Finish the probability model (1 point).

Democrat	Republican	Independent	Other
0.37		0.30	0.02

How would you assign digits to represent each party for a simulation of this sampling process (3 points)?

Democrat =

Republican =

Independent =

Other =

1. The distribution of the number of bedrooms in homes in Canada Bay, New South Wales, Australia in 2021 is below (source: https://profile.id.com.au/canada-bay/bedrooms?es=1&BMID=190). Determine the missing proportion (1 point).

1	2	3	4	5
0.10	0.37	0.31		0.05

What is the expected value for the number of rooms in a home in Canada Bay? _____ rooms (2 points; round your answer to 1 decimal place)

(8) Probability and chance show up a lot in our lives. Knowing the probabilities associated with a certain event can be important for evaluating whether or not you should take a risk. Discuss in few sentences one scenario any adult (not necessarily you specifically) might face where evaluating probability before making a decision would be beneficial (6 points).

(9) Would you consider the following events random or not (recall, we cannot predict outcomes of random events in the short run)? Explain each choice (2 points each).

(a) Turning left at the next stop sign you reach.

RANDOM NOT RANDOM

Why?

(b) Running into a friend from high school at the grocery store.

RANDOM NOT RANDOM

Why?

(c) A home being struck by a tornado.

RANDOM NOT RANDOM

Why?

(d) Completing STAT 1350 with a passing grade.

RANDOM NOT RANDOM

Why?